To solve the equation \( |13 + 4y| = 15 \), we need to handle the absolute value. The absolute value of an expression gives the positive version of that expression. This means there are two possible cases to consider:

### Case 1: 
The expression inside the absolute value is positive or zero:
\[
13 + 4y = 15
\]
Solve for \(y\):
\[
4y = 15 - 13
\]
\[
4y = 2
\]
\[
y = \frac{2}{4} = \frac{1}{2}
\]

### Case 2: 
The expression inside the absolute value is negative:
\[
13 + 4y = -15
\]
Solve for \(y\):
\[
4y = -15 - 13
\]
\[
4y = -28
\]
\[
y = \frac{-28}{4} = -7
\]

### Solution:
The two solutions are:
\[
y = \frac{1}{2} \quad \text{or} \quad y = -7
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve \( |3y - 8| = 12 \).
2. What are the solutions for \( |5 + 2x| = 10 \)?
3. Solve \( |x + 1| = 0 \).
4. How do you solve \( |7x - 3| = 4 \)?
5. What is the value of \(x\) in \( |x - 9| = 2 \)?

**Tip:** When solving absolute value equations, always consider both the positive and negative cases for the expression inside the absolute value.

Learn how to solve the absolute value equation ∣13 + 4y∣ = 15 with step-by-step instructions. This problem explores algebraic concepts like absolute value and linear equation solving. Suitable for students in Grades 8-10.

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